complete bipartite graph
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Input interpretation

complete bipartite graph

Alternate names

complete bicolored graph | complete bicoloured graph | complete bigraph

Definition

A complete bipartite graph, sometimes also called a complete bicolored graph or complete bigraph, is a bipartite graph (i.e., a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent) such that every pair of graph vertices in the two sets are adjacent. If there are p and q graph vertices in the two sets, the complete bipartite graph is denoted K_(p, q). The above figures show K_(3, 2) and K_(2, 5). K_(3, 3) is also known as the utility graph (and is the circulant graph Ci_(1, 3)(6)), and is the unique 4-cage graph. K_(4, 4) is a Cayley graph. A complete bipartite graph K_(n, n) is a circulant graph, specifically Ci_(1, 3, ..., 2⌊n/2⌋ + 1)(n), where ⌊x⌋ is the floor function.
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Related terms

bipartite graph | cage graph | cocktail party graph | complete graph | complete k-partite graph | complete tripartite graph | crown graph | k-partite graph | Thomassen graphs | utility graph | Zarankiewicz's conjecture

Subject classifications

MathWorld

bicolorable graphs | bipartite graphs | class 1 graphs | complete bipartite graphs | connected graphs | distance-regular graphs | distance-transitive graphs | edge-transitive graphs | graceful graphs | triangle-free graphs | k-partite graphs

MSC 2010

05Cxx
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